A college has a functional coffee vending machine. The number of people taking coffee from the machine per day(x) shows a Poisson distribution with a a mean of 100 people per day. For each coffee sold, the vendor gets 2 Rs. However the vendor has to pay a certain rent(r) per day to the college. So the profit per day made by the vendor is Y= 2x- r. Find the value of rent r such that the expected profit per day day is Rs 50. What is the variance in his per day profit?. Explain your reasoning.